x^2-2xy+3y^2=9｛4x^2-5xy+6y^2=30

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 16:56:04

x^2-2xy+3y^2=9｛4x^2-5xy+6y^2=30
x^2-2xy+3y^2=9
｛
4x^2-5xy+6y^2=30

x^2-2xy+3y^2=9｛4x^2-5xy+6y^2=30
x^2-2xy+3y^2=9 ----(1)
4x^2-5xy+6y^2=30 ----(2)
将(1)式乘以10得到
10x^2-20xy+30y^2=90
将(2)式乘以3得到
12x^2-15xy+18y^2=90
两式相减得到
2x^2+5xy-12y^2=0
那么(x+4y)(2x-3y)=0
于是x=-4y或者x=3y/2
如果x=-4y,则(1)式等于16y^2+8y^2+3y^2=9
y^2=1/3,
y=根号3/3,此时x=-4根号3/3
y=-根号3/3,此时x=4根号3/3
如果x=3y/2,（1）式等于（9/4-3+3）y^2=9
则y^2=4,
y=2,此时x=3
y=-2,此时x=-3
所以共有四组解

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